This invention relates to simulation networks and more particularly to a network for simulating a frequency-dependent negative resistor (FDNR) alone or in parallel with a capacitor and/or a resistor.
In order to provide high-quality filters for use in integrated circuit applications, simulation networks are employed to replace filter inductors with other elements that can be fabricated with integrated circuit techniques. One method of realizing a lowpass inductor-capacitor-resistor (LCR) filter network is to use the concept of frequency-dependent negative resistors (FDNR), which are designated by the parameter D and a symbol represented by four parallel lines. An FDNR is a circuit element defined by its admittance Y which satisfies the relationship Y(s) = s.sup.2 D, where s is the complex frequency parameter and D is a real number which may be positive or negative. A prior-art lowpass ladder filter comrpises a pair of series inductors connected in series between input and output terminals, an inductor in series with a capacitor and connected between the junction of the series inductors and a ground reference potential, an output capacitor connected between the output terminal and ground, and input and output resistors connected between the input and output terminals, respectively, and ground. The voltage transfer function of this filter is unchanged if the filter is transformed to an equivalent network by multiplying the admittance of every element by the complex frequency parameter s = j.omega. so that an inductor becomes a resistor, a resistor becomes a capacitor, and a capacitor becomes an FDNR in the transformed equivalent network in accordance with the technique described in the article, "Network Transfer Functions Using the Concept of Frequency-Dependent Negative Resistance" by L. T. Bruton, IEEE Transactions on Circuit Theory, Aug. 1969, pp. 406 - 408. The resultant equivalent network includes an FDNR, the series combination of an FDNR and a resistor, and the parallel combination of an FDNR and a capacitor. Prior-art circuits for simulating an FDNR singularly or in combination with other elements are relatively complex and generally employ two or more amplifiers. Although the structure disclosed in the article, "Parallel Resonator with a Resistance and a Frequency-Dependent Negative Resistance Realized with a Single Operational Amplifier" by Francesco Molo, IEEE Transactions on Circuits and Systems, vol. CAS-21, no. 6, November 1974, pp. 783 - 788, employs only one amplifier, the circuit there has a finite Q in that the reactance of the network cannot be adjusted to zero at a particular frequency. Also, the circuit in this article does not simulate an FDNR alone, and requires three capacitors in the simulation network as opposed to the usual two capacitors.
An object of this invention is the provision of an improved circuit for realizing an FDNR singularly or in parallel combination with a resistor and/or a capacitor.